To determine which form of the ideal gas law is used to calculate the temperature of a gas, we can start by recalling the general form of the ideal gas law:
[tex]\[ PV = nRT \][/tex]
where:
- [tex]\( P \)[/tex] is the pressure of the gas
- [tex]\( V \)[/tex] is the volume of the gas
- [tex]\( n \)[/tex] is the number of moles of the gas
- [tex]\( R \)[/tex] is the ideal gas constant
- [tex]\( T \)[/tex] is the temperature of the gas
We want to solve for the temperature [tex]\( T \)[/tex]. To do this, we need to rearrange the equation to isolate [tex]\( T \)[/tex] on one side. Starting from the ideal gas law:
[tex]\[ PV = nRT \][/tex]
we divide both sides of the equation by [tex]\( nR \)[/tex] to isolate [tex]\( T \)[/tex]:
[tex]\[ T = \frac{PV}{nR} \][/tex]
This shows that the expression for the temperature [tex]\( T \)[/tex] in terms of pressure [tex]\( P \)[/tex], volume [tex]\( V \)[/tex], number of moles [tex]\( n \)[/tex], and the ideal gas constant [tex]\( R \)[/tex] is:
[tex]\[ T = \frac{PV}{nR} \][/tex]
Thus, the correct form of the ideal gas law that can be used to calculate the temperature of a gas is:
[tex]\[ \boxed{B. \ T = \frac{PV}{nR}} \][/tex]
